Maximal bilinear singular integral operators associated with dilations of planar sets |
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| Authors: | Geoff Diestel |
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| Affiliation: | a Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
b Department of Mathematics, University of Missouri, Columbia, MO 65211, USA |
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| Abstract: | We obtain square function estimates and bounds for maximal singular integral operators associated with bilinear multipliers given by characteristic functions of dyadic dilations of certain planar sets. As a consequence, we deduce pointwise almost everywhere convergence for lacunary partial sums of bilinear Fourier series with respect to methods of summation determined by the corresponding planar sets. |
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| Keywords: | Bilinear operators Bilinear Hilbert transform Lacunary almost everywhere convergence |
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